Question

\[\huge Calculas\quad Question\quad Of\quad the\quad DAY\]:
If f is continuous on [m,n] and differentiable for ( m , n ), which of the following could be false?

A) f ' (c) = ( f(n) - f(m) ) / ( m - n ) ) for some c is an element of (m ,n)

B) f ' ( c ) = 0 for some c is an element of [ m , n ]

C) f has a maximum on [ m , n ]

D) f has a maximum on [ m , n ]

E) All of the above are always true

Answer 1

@saifoo.khan @lgbasallote @mathslover @moongazer
can any one solve it

Answer 2

I think it's option A

Answer 3

A doesn't have limits in the definition, so it's not rigorous.

Answer 4

Its A and B (If (a) was (f(n)-f(m))/(n-m) then it would be true since its the statement of the Mean Value Theorem).

B is clearly false, Take f(x) = x as an example. It is continuous and differentiable but nowhere is its derivative 0

Answer 5

First, C&D are the same, they're true
Second, A is false becos the right sentence should be:
\[\huge f ' (c) = ( f(m) - f(n) ) / ( m - n ) ) \]for some c is an element of (m ,n)
yea i missed it B is false too, the prerequisite for B to be true is that \[\huge f(m) = f(n)\]

Answer 6

answer

Answer 7

Alright, I'll give a better response. No expression of the derivative's formal statement as a limit can be configured into a way such that all the slopes can be simplified into the average slope.

Answer 8

aM i RiGhT

Answer 9

Yes, I didn't notice B either. It's wrong as well.

Answer 10

a medal

Answer 11

How do I shot medal?

Answer 12

a medal for me

Answer 13

@mathslover

Answer 14

Can't tell if this is pandering.

Answer 15

okay any one left